On the time value of money equation and its application to risk

The time value of money (TVM) equation is a polynomial therefore it has interest rates as solutions. Until recently, only one of these solutions has been employed in the financial literature. The other solutions have been ignored because they lie elsewhere in the complex plane. This paper shows that working in the complex plane is useful. Previously published results are gathered together and a new conjecture is based on them. The first result is that equations for financial concepts based on the TVM equation can have 'complex twins', alternative equations embedded in the complex plane, and that these complex twins can shed new light on old problems. The second result is that complex twins can be obtained for the mean and variance of a set of data, again using the TVM equation. Finally, the new element, a conjecture is made that a complex twin, based on the TVM equation, exists for the price of an option. If the conjecture is true, the TVM equation would become the core equation for the analysis of all, rather than just some, financial concepts.